Question

ABCD is a square of side 14 cm four congruent circles are drawn in a square touching each other externally and also the service of the square calculate the area of the shaded region​

Answer 1

Answer:

The Area of shaded region is 42.16 cm²

Step-by-step explanation:

Given as :

ABCD is a square

The each side of square ABCD = 14 cm

Area of square = A = side × side

i.e A = 14 cm × 14 cm

Or, A = 196 cm²

Area of square = 196 cm²

Again

Four congruent circles are drawn in a square touching each other externally and also the surface of the square

So, The area of each sector of circle = $\dfrac{\pi r^{2}\Theta }{360^{\circ}}$

where r is the radius of sector = 7 cm

The angle = 90°

So,  area of each sector of circle = $\dfrac{3.14\times 7^{2}\times 90^{\circ}}{360^{\circ}}$

i.e area of each sector of circle = 38.46  cm²

∴ Area of four sector of circle = 4 × 38.46  cm²

i.e Area of four sector of circle = 153.84  cm²

The Area of shaded region = Ares of square - Area of four sector of circle

i.e The Area of shaded region = 196 cm² - 153.84 cm²

∴ The Area of shaded region = 42.16 cm²

Hence, The Area of shaded region is 42.16 cm²  Answer